A direct approach to studying soliton perturbations

Starting with an integrable nonlinear evolution equation, the author investigates perturbations about a one-soliton solution, through the inversion of a linear equation for the first-order correction to the soliton solution. This inversion differs from past methods, as the proposed method takes place in coordinate space, not spectral space, while it employs some of the tools of inverse scattering theory. The method is applied to the Korteweg-de Vries, nonlinear Schrodinger and sine-Gordon equations. The first-order corrections are then obtained.

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